HEFAT2014
10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
14 – 16 July 2014
Orlando, Florida
EXPERIMENTAL STUDY OF THE HEAT TRANSFER IN A FALLING FILM EVAPORATOR:
INFLUENCE OF THE CO-FLOWING VAPOR
Mura E.* †, Åkesjö A.†, Jongsma A. ‡, Innings F‡., Gourdon M.†, Vamling L.†
†
Chalmers University of Technology, department of Heat and Power Technology SE - 412 96 Göteborg
‡
Tetrapak CPS, Heerenveen, The Netherlands
*E-mail: [email protected]
ABSTRACT
INTRODUCTION
A large number of industrial processes are based on the
concentration of liquid products by means of falling-film
evaporation. In the dehydration of dairy products, concentrating
a fluid by evaporating represents one of the most important
steps of the whole drying process. Among the advantages of
this technology is that it is possible to operate within small
temperature differences which results in low heat consumption.
In this sense, it is necessary to increase the amount of removed
water during the falling-film evaporation to reduce the energy
cost of the overall process. However, reducing the fraction of
the solvent leads to an increase in viscosity of the product
which can show non-Newtonian features. This aspect
significantly affects the heat transfer, that is to say, the higher
the solid content, the lower the heat transfer coefficient. One of
the possible solutions to this drawback consists in drawing
maximum benefit from the interaction between the fluid film
and the co-flow of the gaseous phase resulting from the
evaporation process. Unfortunately, accurate studies of the
effect of co-flow on evaporative falling films are very rare and
difficult to perform because of the high costs of the
implementation of a suitable experimental apparatus.
In this work, the experimental study of the influence of the
co-flow on the heat transfer coefficient is presented as a
function of both the solid content and the mass flow rate of the
feed. The experimental set-up, consisting in a unique industrial
pilot scale evaporator, provides the possibility to obtain results
useful for realistic industrial conditions. Tests were conducted
with varying dry solid content from 10 to 50%.
The results show that the co-flow has the effect to decrease
the potential for fouling/poor wetting. Above this, the influence
on the heat transfer is not as large as expected because of the
dominant influence of the viscosity.
The evaporation of falling film is a technology applied in
various industrial fields, from the food to the pulping industry
[1-4], with the aim to maximize the solid content of the feed
product in detriment of the solvent (water in general). The
advantages of this process, which have been presented several
times in literature [5, 6], consist mainly in: short residence time
of the product (3-20 s), since the falling-film is driven by the
gravity that lead to high velocities of the fluid [2]; low process
temperature results in gentle heat treatment preventing
chemical or physical transformation of the product and
relatively high overall heat transfer coefficient. Moreover, the
overall efficiency can also be improved by reusing the removed
vapour in cascade-coupled multi effect evaporation plants. The
falling film evaporation represents one of the most important
steps in the overall drying process of dairy products where the
product is concentrated up to approximately 50% of dry solid
content (DC), with the dry solid content defined as:
[ ]
[
⁄
]
(1)
In contrast, processes of dehydration that normally follow
this stage are highly energy intensive. For these reasons, the
amount of water removed during this phase of the process
should be as large as possible: under specific conditions, it is
theoretically possible to save about 10% of the energy
consumption of an evaporator-dryer plant by increasing the
total solid content of the concentrate from 48 to 54% [7].
Unfortunately, the higher the DC of the product is the higher its
viscosity. Experimental studies have shown that up to about
37% of DC, the fluid behaves in agreement with the Newtonian
law but with increasing DC, the rheological features fit well
with the Power law model and at 48% DC or higher with the
1938
Hershel-Bulkley yield stress model [8]. At constant mass flow
rate, this increase in viscosity can generate instability in the
falling-film that can lead to the breakdown of the film and
eventually the formation of dry patches. This phenomenon is
associated with a reduction of the heat transfer coefficient (h).
The presence of a co-flow, has been identified as one of the
main factor affecting the heat transfer coefficient [9, 10].
Mathematical models present in the literature are still
immature or insufficient to describe this phenomenon.
Furthermore, the lack of adequate experimental systems makes
the collection of reliable data difficult since they are so far
often taken from industrial installations with the intrinsic
negative effects on the accuracy and on the required times
resources.
In the present work, quantitative results concerning the
influence of the co-flow on the heat transfer coefficient are
presented in function of the dry solid content of the product that
varies from 10 to 50% and in function of its mass flow rate.
The experimental campaign has been performed using an
industrial pilot scale falling film evaporator and results are
supported by images of the falling fluid film obtained by a high
speed image acquisition device.
EXPERIMENTAL SET UP
The experimental set-up consists of a stainless steel tube of
length L = 4.5 m, diameter Ø = 60mm and a thickness δt =
5mm, equipped with a series of thermocouples located on both
the inner (Ti) and the outer surface (To). Differently from the
most common falling film evaporators, our configuration
allows the viewing of the falling film since the product flows in
the outer surface of the tube (heat transfer surface A = 0.85m2).
After being evenly spread by means of an overflow distributor
located on the upper part of the tube, the film achieves rapidly
the saturation conditions and starts to evaporate. The vapor
produced is then condensed and reintroduced into the circuit to
maintain the dry solid content (DC) constant. The end of the
tube is provided with a special cup where the temperature of the
processed product (Tsat) is measured with a thermocouple
before it is finally collected. The mass flow rate, the density
and the viscosity are measured in real time before the
introduction of the product into the evaporator.
A source of saturated steam is positioned on the inside of
the tube and distributed homogeneously over its entire length.
That steam, condensing upon the wall, supplies the required
heat for the evaporation process (see Figure 1).
NOMENCLATURE
A
DC
D
fi
g
h
L
k
K
n
P
T
Q
u
U
A,b,c,d,f,g
Nu
Re
Special characters
Ø
δ
ρ
ν
̇
τ
Γ
μ
Subscripts
Avg
app
CF
FF
i
o
sat
Steam
t
tot
w
y
µ3450s-1
[m2]
[%]
[m]
[-]
[ms-2]
[Wm-2K-1]
[m]
[Wm-1K-1]
[Pasn]
[-]
[Pa]
[K]
[W]
[ms-1]
[Wm-2K-1]
[-]
[-]
[-]
Surface
Dry solid content
Characteristic diameter
Friction coefficient
Gravity acceleration
Local heat transfer coefficient
Length
Conductivity
Consistency factor
Power low index
Pressure
Temperature
Heat flux
Velocity
Overall heat transfer coefficient
Parameters
Nusselt number
Reynolds number
[m]
[m]
[kgm-3]
[m2s-1]
[s-1]
[Pa]
[kgm-1s-1]
[Pas]
Diameter
Thickness
Density
Kinematic viscosity
Shear rate
Shear stress
Mass flow rate per unit width
Dynamic viscosity
Averaged
Apparent
Co-flow
Falling film
Inside
Outside
Saturation
Steam inside of the tube
Tube
Total
Wall
Yield stress
Measured viscosity at ̇
Figure 1. Schematic diagram of the evaporator: DI=
density meter, FI=flow meter, VI=viscometer.
The volume of condensate produced per unit of time is used
to characterize the heat flux (Q). A more detailed description of
the experimental system, including the calibrations procedure
of measurement systems, is available in [4, 11].
To study the influence of the co-flow on the falling film, an
amount of steam is injected from the top of the evaporator (see
1939
Figure 1). The largest part of the total vapor co-flowing (~70%)
consists of vapor that has been released during the process and
recycled by means a steam ejector. The remaining fraction is
supplied from an external source. The steam is forced to flow in
contact with the falling film by means of a transparent Plexiglas
shell that has been fixed around the tube. The distance between
the internal Plexiglas surface and the external tube surface is of
25mm.
(3)
(4)
where: a=4∙10-7, b=30, c=6∙10-5, d=17,5.
n (in our case n ≤ 1) represents the non-linear feature of the
correspondence between an applied shear stress and the
response in terms of shear rate. This index, varying from value
close to unity typical of Newtonian fluids, is reduced by
increasing DC. A simple approximation, valid in the range of
our interest (16 ≤ DC ≤ 60%), has been obtained on the basis of
the rheometer’s data:
METHOD
Samples
The feed material for the experiments is composed of a
dairy powder and distilled water in several different mass
fractions as shown in table 1. The product tested in this study is
related to whole milk and its properties are similar to
reconstituted whole milk. The dry solid content is obtained by
drying a sample in an oven (T = 105 ° C for t ≥ 24h), and
comparing that to its original total wet mass. The measurement
is done twice for each sample and an averaged value is
reported. As already anticipated in the introduction, the
viscosity of the feed depends on the dry solid content and both
the hydrodynamics and the heat transfer mechanisms are
obviously affected by this feature.
The dynamic viscosity has been measured by an online
viscometer at constant shear rate (3450 s-1). Values, reported in
Table 1, demonstrate the increase of the viscosity as a function
of the solid content.
(5)
where: f=3 and g=3,5. The experimental results and the trend
of these three parameters as a function of the solid content are
shown in the graph of Figure 2.
Other types of similar approximations are present in the
literature [8].
1
4,3
1,2
0,9
1,6
1,4
(n < 1)
K
n
Tau
k model
n model
Tau model
3
0,4
2
0,2
0
0,25
1
0,35
0,45
0
0,55
Solid Content
This result has been further confirmed by an experimental
rheological study performed by a rheometer Rheoplus 32
equipped with a coaxial cylinder sensor kept at the same
temperature of the evaporative process (55°C). These tests,
carried out in function of the DC, provided the shear stress [Pa]
evolution as a function of the shear rate varying from 0 to 1000
[s-1]. The rheometer results reveal that our product can be
identified, depending on its solid content, by three parameters
typical of the Herschel-Bulkley model. This model is
characteristic of yield-shear-thinning fluids according to the
equation:
̇
4
0,6
Tau [Pa]
- n
K [Pasn]
DC [%] 51,5 51 49 42 27,7 25,5 24 16 15 14 11
ρ [kg/m3] 1120 1120 1115 1100 1057 1057 1055 1030 1025 1022 1016
4,6
5
0,8
Table 1: Dry solid content (DC), Density (ρ) and online
measured viscosity (μ3450s-1).
μ3450s-1[mPa∙s] 221 172 82,9 46,5 6,7
6
Figure 2: Experimental and fitted values of Yield stress,
Consistency factor and n-index as a function of the solid
content of the dairy product.
Other characteristic parameters of the product, such as
thermal conductivity (k) and heat capacity (Cp), have been
obtained, as a function of the temperature (T) and the solids
content (DC), by means of correlations present in the literature
[12].
Experimental Protocol
The goal of this research is to highlight the influence of the
co-flow on the mechanism of heat transfer during the
evaporation process of the fluid falling film. In order to achieve
this, the system is preheated (at temperature close to 55°C)
under vacuum conditions (Pabs ~ 0.016 MPa) by means of
steam. The product (c.a. 50kg), mixed in the suited proportions
of solvent (water) and dry solid content, is pumped into the
plant, forced to flow along the tube and heated by means of
condensing steam on the inside of the tube. At this point a
(2)
where τy [Pa] represents the yield stress which appears for DC
≥ 40% (below this value, τy vanishes and the model takes the
power low form). The parameter K [Pa∙sn] is the consistency
factor and it assumes the dimensions of a viscosity depending
on the index n, which is <0 for shear-thinning fluids. In our
case, the variation of these parameters fits very well with an
exponential law of DC with the expressions:
1940
difference of temperatures (ΔT) between the two fluids is
applied and the evaporative process starts. When the operating
conditions (flow rate and temperatures of the falling fluid and
temperature of steam) are stable, data related to the heat
transfer are recorded. The concentration of the product is kept
constant thanks to the continuous recirculation of the
condensate produced during the evaporation and a sample of
product is extracted during the phase of the measurement for
the analysis of the rheological characteristics and of the solid
content. After the measurement has been obtained, a mass flow
rate of 0,039kgs-1 of co-flowing steam with a density of
ρsteam=0,11kgm-3 is circulated with an averaged velocity (uCF)
of 55m/s as shown in Figure 1. When the new stable conditions
are achieved, values of heat transfer are recorded.
The same tests were carried out in non-evaporative
conditions (ΔT=0) with the objective to observe the effect of
co-flowing steam on the appearance of falling-film
hydrodynamic, by using a high speed image acquisition device
(500fps-1). The images capturing has been an important part of
this work although their contribution is highly qualitative. The
images have been acquired during the experimental tests when
stable conditions were obtained and both with and without coflowing vapor. The pictures have been taken at three different
levels (0,4 - 2 - 4 m from the distributor).
⁄
l is the viscous characteristic length, defined by
( )
When the co-flow is active, due to the sum of static head,
kinetic energy of the steam and frictional losses, a pressure
drop occurring all along the tube [6]. This pressure drop ΔP
(measured as shown in Figure 1) results in a variation of the
saturation temperatures (Tsat) of the product leading to a higher
thermal driving force (ΔT) at the bottom of the evaporator
compared to the upper side. Since in our system (as in every
industrial plants) the value of the Tsat is collected in the lower
part of the evaporator, it is necessary to make a correction to
obtain a representative value of the thermal driving force for
the entire evaporation process. Assuming that the pressure drop
is linear, a saturation temperature profile was calculated and an
average value of Tsat was determined.
To be able to compare the heat transfer measurements, it is
necessary to define a viscosity that takes into account the nonNewtonian features of the film. We will call this the apparent
viscosity (µapp). To obtain this value the thickness of the fluid
film must be evaluated (see Figure 3).
ANALYSIS
Heat transfer evaluation
To evaluate the influence of the co-flow on the heat transfer
mechanism we choose to refer to the overall heat transfer
coefficient (U) defined as
(6)
where Ai represents the inside area of the tube and hi is the
inside heat transfer coefficient obtained by using the Schnabel
& Palen relation for vertical falling film [13]. δw is the wall
thickness, kw is the conductivity of the tube wall and Aavg is the
associated logarithmic averaged area. The only unknown
parameter is the outside heat transfer coefficient ho.
These values are calculated by using the total heat flux Qtot,
obtained by measuring the steam condensate flow, in agreement
with the relation:
Figure 3. Qualitatively velocity profile of the falling film
(black lines) and co-flowing vapor (gray lines).
Under the hypothesis of a laminar flow on a flat surface
with small film thickness compared to the tube length, for a bidimensional case, we can integrate the momentum flux (τrz)
considering the effect of the co-flowing vapor shear stress upon
the interface as boundary condition:
(7)
{
Tsteam and Tsat represent respectively the steam temperature
and the saturation temperature of the falling film.
Others tools such as the Nu end Re numbers are used to
evaluate the convective exchange in the area of the product and
the flow condition:
(10)
where τCF represent the momentum flux of the co-flowing
vapor acting on the free falling film surface defined by [14]:
(11)
(8)
where fi is the friction coefficient calculated by considering the
ΔP
(9)
1941
These images have been captured on the lowest optical
access of the evaporator (4m from the distributor) at the final
section of the Plexiglas tube. As is observable, it seems that
there is no difference in the appearance of the falling film. This
result is also valid for product with higher solid content.
We are now able to show in the graph of Figure 5 the
variation of the heat transfer coefficient (ho) as a function of the
viscosity (μapp). As can be observed, a drastic reduction of the
heat transfer coefficient corresponds to an increase in viscosity.
This trend is valid in both cases of co-flow and no-co-flow.
(12)
and uCF-FF is the velocity of the co-flowing vapor relatively to
the falling film velocity.
Substituting equation (2) on the momentum flux equation
resulting from (10) it is possible to integrate the velocity profile
over the film thickness from 0 to δ and to obtain the specific
mass flow rate (Γ) according to the equation:
[(
)
(
)
]
(13)
In (13) the only unknown parameter is the film thickness
(δ). The effect of τCF is negligible when co-flowing vapor is not
applied (uCF-FF≈0). With δ obtained from (13), in agreement
with the classical Nusselt’s theory, we can calculate an
apparent viscosity (µapp) of a Newtonian fluid without
interfacial shear stress having equal film thickness:
(14)
RESULTS
Images
It has been observed that, the “Wind Over Water” effect,
shown by Jebson & Chen [10], generated by the momentum
sheared between falling film and co-flow that should improve
the convective heat transfer, it seems to be present only in the
first section of the falling process close to the distributor. After
this section, the flow does not appear to have any apparent
effect. Moreover, the small difference observed seems to be
typical of the case with low solid content: by increasing the
DC, the surface effects seem to vanish gradually.
In Figure 4, two pictures with and without co-flow are
presented with DC=25.5% and Γ=0,16kgm-1s-1.
Figure 5. Experimental results of the heat transfer
coefficient (ho) Vs viscosity (μapp) in co-flow and no-co-flow
conditions.
The areas that contain the points obtained in the different
conditions of co-flow and no-co-flow are almost overlapping:
the trends of variation of ho follow the same pattern. This
means that there is not an obvious effect of the co-flow on the
heat transfer coefficient above decreasing the apparent
viscosity. As a matter of the fact, points related to the case with
co-flow are shifted toward lower values of the apparent
viscosity if compared with the no-co-flow results. This aspect
highlights that for a constant (DC), the action of τCF has the
effect of reducing the contribution of the viscous forces acting
on the fluid film promoting its fall. The points within the
continuous circle in Figure 5, whose corresponding values are
shown in Table 2, are eloquent of this aspect.
Table 2: Apparent viscosity (μapp), film thickness (δ)
obtained form (13), and heat transfer coefficient (ho) at the
same solid content (DC) for co-flowing and no-co-flowing
conditions.
DC [%]
Figure 4. Image of a fluid with DC=25,5%, flowing at
mass flow rate of Γ=0,16kgm-1s-1, without evaporation,
respectively in reduced co-flow (right) and no-co-flow
condition (left).
27,7
1942
Condition
δ [mm]
µapp[mPas]
ho[Wm-2k-1]
Co-Flow
Co-Flow
No-Co-Flow
No-Co-Flow
0,76
0,98
0,85
1,11
4,73
5,02
6,67
6,63
2600
2470
2400
2320
The effect of the co-flow was also investigated by analyzing
the local difference in temperature (between the inner and the
outer side of the tube) at different levels of the evaporator and
observing the images acquired during the experimental tests.
This analysis led to associate a more strict condition of poor
wettability to the no-co-flow conditions. It means that higher
specific mass flow rates (Γ) are required to assure the minimum
wettability condition. The adverse consequence of this aspect
mainly consists in the formation of dry spots on the external
wall surface. In this condition, the heat transfer coefficient is
affected by the drastic reduction. This aspect is observable in
Figure 6 where the variation of the local heat transfer
coefficients, at different distance from the inlet distributor (0,1 3 -3,5 and 4,1 m), is reported versus time.
co-flow, previously attributed to the momentum traveling down
the tube [9, 10], seem to show another nature.
Indeed, the images show not any obvious effects of the coflow on the free surface of the film even if it is evident the
positive effect on the reduction of fouling. In this sense, the
evaluation of the apparent viscosity of the falling film
highlights the role played by the co-flow on the increasing of
the heat transfer coefficient.
2,00
no-co-flow
Nu
1,20
0,80
co-flow
2500
hlocal [Wm-2K-1]
No co-flow
1,60
Chart Title
3000
Co-flow
Fouled
0,40
2000
0,00
10
1000
Figure 7. Nusselt Vs Reynolds numbers for co-flow and noco-flow conditions.
1000
500
0
5,10
100
Re
1500
5,60
6,10
0,10 m
3m
3,5 m
4,1 m
6,60
This line of reasoning makes us think that the influence of
the co-flow should be associated with variations in the surface
tension forces (i.e. Marangoni) on a smaller scale of the film
thickness. This assertion is reflected mathematically and
experimentally in some studies [15, 16] in which have been
highlighted that instabilities of the interface liquid-gas are
amplified or damped by the combined action of the heat and the
gas flow field.
7,10
t [h]
Figure 6. Variation of local heat transfer coefficients on the
tube Vs time: effect of the co-flow on the wettability (the noco-flow corresponds to the left point identified as Fouled in
Figure 5).
CONCLUSIONS
As can be observed, the local heat transfer coefficient on the
highest section of the evaporator (0,1 m) is not affected by the
presence of the co-flow, since the flow is still evenly distributed
around the tube. As a matter of fact, the most relevant results
concern the variation of the local heat transfer coefficient on
the lower sections of the tube (3 – 3,5 – 4,1 m) , which are more
sensible to the conditions of reduced wettability. For these
cases, it is easy to notice that the co-flow condition is
characterized by a drastic increasing of the heat transfer
coefficient if compared with the no-co-flow conditions. This
behavior underlines that the presence of dry spots on the outer
surface of the evaporator is reduced when the co-flow is active.
This aspect can be highlighted by taking into account the
dimensionless numbers of Nu end Re for the falling film as
shown on the Figure 7.
The solution to this problem consists in increasing the
specific mass flow rate that it is to say the minimum limit of
wettability is shifted towards higher values. This could
encourage some reflections whereas the positive effect of the
In this paper, the experimental study of the influence of the
co-flow on the overall heat transfer coefficient has been
investigated. The work has been performed by means of an
industrial falling film evaporator pilot plant. Several samples of
a dairy product have been tested in function of the solid content
(DC) varying from 11% to 51%. Results show that the increase
in solid content leads to a dramatic increment of the viscosity of
the feed.
Rheological measurements have shown that the fluid shows
non-Newtonian characteristics in the cases of high solid
content. This aspect heavily influences the heat transfer
coefficient.
It has been shown that the co-flow has a positive impact on
the heat transfer coefficient. This effect is reduced for
increasing values of DC until it almost vanishes.
The positive effects of the co-flow is related to two facts: 1)
it reduces the effects of fouling ensuring the wettability at low
values of specific mass flow rate and 2) it reduces the apparent
viscosity of the falling film under co-flowing condition (i.e.
1943
lower apparent viscosity than in no-co-flow condition) which
inherently increase heat transfer.
In perspective, it is desirable to further investigate the
effects of the co-flow on the surface tension forces.
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1944